The Mexican banker running to head the International Monetary Fund warned Monday that the agency could face a conflict of interest if his chief rival, a European, was appointed to the top job in the midst of the financial crisis roiling Europe.

Mexican Central Bank chief Agustin Carstens, who was in Washington to lobby for the IMF post, said the agency needs to be seen as guarding the interests of all its members, not just those of the Europeans.

Carstens’s chief competitor, French Finance Minister Christine Lagarde, is considered the front-runner to replace Dominique Strauss-Kahn, who resigned last month as managing director to fight sexual assault charges in New York. Lagarde has been deeply involved in the European debate about how to keep the Greek government from defaulting on its loans and how to help other strapped economies, such as Ireland and Portugal.

Carstens’s appearance Monday at the Peterson Institute for International Economics — before a crowd that included IMF board members, U.S. government officials and influential economists — made clear that he would see his long-shot candidacy to the end.

Rather than backing down, Carstens used the lunch address to criticize Europe’s dominance of the agency and cautioned that the IMF must work to maintain its credibility among developing countries.

“The fund can’t be perceived as working for Europeans,” he said. “I am sure she [Lagarde] will say she is working for the fund. But that question will be there.”

Carstens argued that Europe has been lax in policing its economy and slow to impose the sort of program on Greece — whether a restructuring of its debts or speedy economic reform — that would restore growth and investor confidence. As an outsider, he said, his candor could help cut through the political and economic issues that Europe has found difficult to resolve.

Recent loans to Greece, Ireland and Portugal have been the largest in IMF history. Carstens said continuing European control of the agency’s executive suite means “we could have a situation where borrowers dominate the institution.”

Lagarde, a private-sector lawyer for most of her career, has not said whether she would recuse herself from discussions over Greece or other issues on which she has taken a position or that are of direct interest to the French economy or French financial firms.

The prospect of a Greek default — now judged as increasingly likely by ratings agencies such as Standard & Poor’s, which have steadily downgraded the quality of Greek bonds — is perhaps the most acute issue facing the IMF right now. If Greece cannot make its bond payments, it could put major European and U.S. banks at risk.

The competition between Carstens and Lagarde has become a referendum on oversight of a world economy in which growth has shifted toward developing giants such as China, while Europe and the United States struggle.

Major European countries endorsed Lagarde soon after Strauss-Kahn’s resignation, setting aside earlier pledges to scrap their 60-year-old hold on the job and choose the next IMF head through an open and merit-based process.

Carstens said that he felt as if he was “starting a soccer game [down] five to nothing” and that the likelihood of Lagarde winning is “quite high.”

Bank of Israel chief Stanley Fischer’s name was put forward, but he was not included in the list of finalists that the IMF board will interview. He is 67, and IMF rules do not allow the appointment to a full term of anyone older than 65. A source familiar with the deliberations said there was not adequate support for Fischer to propose changing the bylaws.

Still, the Mexican banker, a University of Chicago-trained economist who has held top staff positions at the IMF, said his candidacy was an important step for developing economies that want more say in international institutions.

“What I am trying to provide is options,” Carstens said. “If they don’t want to decide on merit, that is their choice. But it is not because there weren’t options.”

Carstens met Monday morning with Treasury Secretary Timothy F. Geithner. The United States, which holds 16 percent of the votes on the IMF’s executive board, has remained uncommitted in the race. A Treasury spokesperson said Geithner considered Carstens an “exceptionally capable candidate.”

Carstens said that Geithner reiterated to him that the United States had not made a choice and that the situation was “very fluid.”